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Scientific Journal of Samarkand University

Abstract

The process of anomalous solute transport in a coaxial cylindrical porous media is modelled by differential equations with a fractional derivative. The problem of solute transport in a two-zone cylindrical media consisting of macro- and micropores taking into account adsorption effectshas been numericallyposed and solved. The concentration profiles of suspended particles and the adsorbed solute in the macropore and micropore, the surface of the local concentration in the micropore are determined. The influence of adsorption phenomena and the order of the derivative with respect to the coordinate, i.e. fractal dimension of the media, on the characteristics of the solute transport in both zones is established

First Page

32

Last Page

46

References

1. Van GenuchtenM.Th., Tang D. H. Some Exact Solutions for Solute Transport Through Soils Containing Large Cylindrical Macropores // Water Resources Research. Vol. 20. No. 3. 1984. Pp. 335-346. 2. Rao P.S.C., Jessup J. E., Rolston D.E., Davidson J.M., Kilgrease D.P. Experimental and mathematical description of nonadsorbed solute transfer by diffusion in spherical aggregates // Soil Sci. Soc. Am. J., Vol. 44. 1980a. Pp. 684 – 688. 3. Rao P.S.C., Jessup R.E., Addison T.M. Experimental and theoretical aspects of solute diffusion in spherical and non-spherical aggregates // Soil Sci. Soc. Am. J., 133. 1982. Pp. 342-349 4. Rao P.S.C., Rolston D.E., Jessup R. E., Davidson J.M. Solute transport in aggregated porous media: Theoretical and experimental evaluation. // Soil Sci. Soc. Am. J., Vol. 44. 1980b. Pp. 1139 – 1146. Scotter D.R. Preferential solute movement through large soil voids, I. Some computations using simple theory // Australian Journal of Soil Research Vol. 16. 1978. Pp. 257-267. 5. Skopp J., Warrick A.W. A two-phase model for the miscible displacement of reactive solutes in soil // Soil Sci. Soc. Am. J. 38(4). 1974. Pp. 545-550. 6. Sudicky E.A., Frind E.O. Contaminant transport in fractured porous media: Analytical solutions for a system of parallel fractures // Water Resour. Res. 18(6). 1982. Pp.1634-1642. 7. Tang D.H., Frind E.O., Sudicky E.A. Contaminant transport in fractured porous media: Analytical solution for a single fracture // Water Re sour. Res. 17(3). 1981. Pp. 555-564. 8. Coats, K.H., Smith, B.D. Dead-end volume and dispersion in porous media // Society of Petroleum Engineering Journal, 4(1), 1964, 73-84. 9. Gaudet J.P., Jegat H., Vachaud G., Wierenga P. Solute transfer with exchange between mobile and stagnant water through unsaturated sand // Soil Sci. Soc. Am. J., 41, 665-671, 1977. 10. Nkedi-Kizza P., Biggar J.W., Selim H.M., van Genuchen M.Th., Wierenga P.J., Davidson J.M., Nielsen D.R. On the equivalence of two concentual models for describing ion exchange during transport through an aggregated oxisol // Water Resour. Res. 20:1123-1130, 1984. 11. Rezanezhad F., Jonathan S.P., James R.G. The effects of dual porosity on transport and retardation inpeat: A laboratory experiment // Can. J. Soil Sci. 92. 2012. 723-732 p. 12. Selim H.M. Transport & Fate of Chemicals in Soils: Principles & Applications. CRC Press Taylor & Francis Group. Boca Raton London New York. 2015. 13. Skopp J., Gardner W.R., Tyler E.J. Solute movement in structured soils: Two-region model with small interaction // Soil Sci. Soc. Am. J., 45, 837-842, 1981. 14. Van GenuchtenM.Th.,Werenga P.J. Mass Transfer Studies in Sorbing Porous Media: II. Experimental Evaluation with Tritium (H2O) // Soil Sci. Soc. American J., Vol. 41, 1977. 272-278 p. 15. Van GenuchtenM.Th.,Wierenga P.J. Mass transfer studies in sorbing porous media. 1. Analytical solutions // Soil Sci. Soc. Am. J., 40(4), 1976, 473-480. 16. Villermaux J., and W. P. M. van Swaajj, Modelerepre"sentatif de la distribution des temps de sejourdansunre"acteur semi-infmi a dispersion axiale avec zones stagnarites. Application aI'fecoule-mentruisselant des colonnesd'anneauxRaschig // Chem. Eng. Sci.,24, 1097-1111, 1969. 17. Nigmatullin R. R. The realization of the generalized transfer equation in a medium with fractal geometry. Phys. Stat. Sol. (b). 133. 1986. 425–430. 18. Fomin S., V. Chugunov and T. Hashida. Application of Fractional Differential Equations for Modeling the Anomalous Diffusion of Contaminant from Fracture into Porous Rock Matrix with Bordering Alteration Zone. Transport in Porous Media. 81, 2010.187–205. 19. Fomin S., V. Chugunov and T. Hashida. Mathematical modeling of anomalous diffusion in porous media. Fractional Differential Calcules. Volume 1, Number 1. 2011. 1–28. 20. Fomin S., V. Chugunov and T. Hashida. The effect of non-Fickian diffusion into surrounding rocks on contaminant transport in fractured porous aquifer. Proceedings of Royal Society A461, 2923–2939, 2005. 21. Bear J. Dynamics of Fluids in Porous Media. American Elsevier Publishing Co., New York. 1972. P.761. 22. Van GenuchtenM.Th., Tang D. H. Some Exact Solutions for Solute Transport Through Soils Containing Large Cylindrical Macropores // Water Resources Research. Vol. 20. No. 3. 1984. Pp. 335-346. 23. Beybalayev V.D., Shabanova M.R. Chislenniy metod resheniya nachalno-granichnoy zadachi dlya dvumernogo uravneniya teploprovodnosti s proizvodnimi drobnogo poryadka // Vestnik Samarskogo gosudarstvennogo texnicheskogo universiteta. Seriya Fiziko-matematicheskiye nauki. 2010. Vipusk 5(21). S. 244–251.

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